getfem_export.h

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/* -*- c++ -*- (enables emacs c++ mode) */
/*===========================================================================

 Copyright (C) 2001-2017 Yves Renard, Julien Pommier

 This file is a part of GetFEM++

 GetFEM++  is  free software;  you  can  redistribute  it  and/or modify it
 under  the  terms  of the  GNU  Lesser General Public License as published
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 (at your option) any later version along with the GCC Runtime Library
 Exception either version 3.1 or (at your option) any later version.
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 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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 License and GCC Runtime Library Exception for more details.
 You  should  have received a copy of the GNU Lesser General Public License
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===========================================================================*/

/**@file getfem_export.h
   @author  Yves Renard <Yves.Renard@insa-lyon.fr>,
   @author  Julien Pommier <Julien.Pommier@insa-toulouse.fr>
   @date October 15, 2001.
   @brief Export solutions to various formats.
*/
#ifndef GETFEM_EXPORT_H__
#define GETFEM_EXPORT_H__

#include "getfem_interpolation.h"
#include "getfem_mesh_slice.h"
#include <list>

namespace getfem {

  /* ********************************************************************* */
  /*                                                                       */
  /*  Save a solution in a file with a Pk interpolation.                   */
  /*                                                                       */
  /* ********************************************************************* */

  inline std::string remove_spaces(const std::string &s) {
    std::string s2(s);
    for (unsigned i=0; i < s.size(); ++i)
      if (s2[i] <= ' ') s2[i] = '_';
    return s2;
  }

  /** @brief VTK export.

      export class to VTK ( http://www.kitware.com/vtk.html ) file format
      (not the XML format, but the old format)

      A vtk_export can store multiple scalar/vector fields.
  */
  class vtk_export {
  protected:
    std::ostream &os;
    char header[256]; // hard limit in vtk
    bool ascii;
    const stored_mesh_slice *psl;
    std::unique_ptr<mesh_fem> pmf;
    dal::bit_vector pmf_dof_used;
    std::vector<unsigned> pmf_mapping_type;
    std::ofstream real_os;
    dim_type dim_;
    bool reverse_endian;
    enum { EMPTY, HEADER_WRITTEN, STRUCTURE_WRITTEN, IN_CELL_DATA,
           IN_POINT_DATA } state;

    template<class T> void write_val(T v);
    template<class V> void write_vec(V p, size_type qdim);
    template<class IT> void write_3x3tensor(IT p);
    void write_separ();

  public:
    typedef enum { VTK_VERTEX = 1,
                   VTK_LINE = 3,
                   VTK_TRIANGLE = 5,
                   VTK_PIXEL = 8,
                   VTK_QUAD = 9,
                   VTK_TETRA = 10,
                   VTK_VOXEL = 11,
                   VTK_HEXAHEDRON = 12,
                   VTK_WEDGE = 13,
                   VTK_PYRAMID = 14,
                   VTK_QUADRATIC_EDGE = 21,
                   VTK_QUADRATIC_TRIANGLE = 22,
                   VTK_QUADRATIC_QUAD = 23,
                   VTK_QUADRATIC_TETRA = 24,
                   VTK_QUADRATIC_HEXAHEDRON = 25,
                   VTK_QUADRATIC_WEDGE = 26,
                   VTK_QUADRATIC_PYRAMID = 27,
                   VTK_BIQUADRATIC_QUAD = 28,
                   VTK_TRIQUADRATIC_HEXAHEDRON = 29,
                   VTK_BIQUADRATIC_QUADRATIC_WEDGE = 32 } vtk_cell_type;
    vtk_export(const std::string& fname, bool ascii_ = false);
    vtk_export(std::ostream &os_, bool ascii_ = false);

    /** should be called before write_*_data */
    void exporting(const mesh& m);
    void exporting(const mesh_fem& mf);
    void exporting(const stored_mesh_slice& sl);

    /** the header is the second line of text in the exported file,
       you can put whatever you want -- call this before any write_dataset
       or write_mesh */
    void set_header(const std::string& s);
    void write_mesh();

    /** append a new scalar or vector field defined on mf to the .vtk file.  If
        you are exporting a slice, or if mf != get_exported_mesh_fem(), U will
        be interpolated on the slice, or on get_exported_mesh_fem().

        Note that vectors should be written AFTER scalars, and tensors
        after vectors

        NO SPACE ALLOWED in 'name' */
    template<class VECT> void write_point_data(const getfem::mesh_fem &mf,
                                               const VECT& U0,
                                               const std::string& name);

    /** append a new scalar or vector field to .vtk file. The Uslice vector is
        the field interpolated on the exported mesh_slice This function should
        not be used if you are not exporting a slice!  NO SPACE ALLOWED in
        'name' */
    template<class VECT> void write_sliced_point_data(const VECT& Uslice,
                                                      const std::string& name,
                                                      size_type qdim=1);
    /** export data which is constant over each element. You should not use
        this function if you are exporting a slice.  U should have
        convex_index().card() elements.  */

    template<class VECT> void write_cell_data(const VECT& U,
                                              const std::string& name,
                                              size_type qdim = 1);
    /** export a data_set correspounding to measures of quality for each convex
        of the supplied mesh (which should have the same number of convex than
        the one used in the vtk_export)

        If a slice is being exported, the convex quality is written as
        point_data (TO IMPROVE ONEDAY), if a mesh/mesh_fem is being exported,
        it is written as cell_data
    */
    void write_mesh_quality(const mesh &m);
    void write_normals();
    const stored_mesh_slice& get_exported_slice() const;
    const mesh_fem& get_exported_mesh_fem() const;
  private:
    void init();
    void check_header();
    void write_mesh_structure_from_slice();
    void write_mesh_structure_from_mesh_fem();
    void switch_to_cell_data();
    void switch_to_point_data();
    template<class VECT> void write_dataset_(const VECT& U,
                                             const std::string& name,
                                             size_type qdim,
                                             bool cell_data=false);
  };

  template<class T> void vtk_export::write_val(T v) {
    if (ascii) os << " " << v;
    else {
      char *p = (char*)&v;
      if (reverse_endian)
        for (size_type i=0; i < sizeof(v)/2; ++i)
          std::swap(p[i], p[sizeof(v)-i-1]);
      os.write(p, sizeof(T));
    }
  }

  template<class IT> void vtk_export::write_vec(IT p, size_type qdim) {
    float v[3];
    for (size_type i=0; i < qdim; ++i) {
      v[i] = float(p[i]);
    }
    for (size_type i=qdim; i < 3; ++i) v[i] = 0.0f;
    write_val(v[0]);write_val(v[1]);write_val(v[2]);
  }

  template<class IT> void vtk_export::write_3x3tensor(IT p) {
    float v[3][3];
    memset(v, 0, sizeof v);
    for (size_type i=0; i < dim_; ++i) {
      for (size_type j=0; j < dim_; ++j)
        v[i][j] = float(p[i + j*dim_]);
    }
    for (size_type i=0; i < 3; ++i) {
      for (size_type j=0; j < 3; ++j) {
        write_val(v[i][j]);
      }
      if (ascii) os << "\n";
    }
  }

  template<class VECT>
  void vtk_export::write_point_data(const getfem::mesh_fem &mf, const VECT& U,
                                    const std::string& name) {
    size_type Q = (gmm::vect_size(U) / mf.nb_dof()) * mf.get_qdim();
    size_type qdim = mf.get_qdim();
    if (psl) {
      std::vector<scalar_type> Uslice(Q*psl->nb_points());
      psl->interpolate(mf, U, Uslice);
      write_dataset_(Uslice, name, qdim);
    } else {
      std::vector<scalar_type> V(pmf->nb_dof() * Q);
      if (&mf != &(*pmf)) {
        interpolation(mf, *pmf, U, V);
      } else gmm::copy(U,V);
      size_type cnt = 0;
      for (dal::bv_visitor d(pmf_dof_used); !d.finished(); ++d, ++cnt) {
        if (cnt != d)
          for (size_type q=0; q < Q; ++q) {
            V[cnt*Q + q] = V[d*Q + q];
          }
      }
      V.resize(Q*pmf_dof_used.card());
      write_dataset_(V, name, qdim);
    }
  }

  template<class VECT>
  void vtk_export::write_cell_data(const VECT& U, const std::string& name,
                                   size_type qdim) {
    write_dataset_(U, name, qdim, true);
  }

  template<class VECT>
  void vtk_export::write_sliced_point_data(const VECT& U,
                                           const std::string& name,
                                           size_type qdim) {
    write_dataset_(U, name, qdim, false);
  }

  template<class VECT>
  void vtk_export::write_dataset_(const VECT& U, const std::string& name,
                                  size_type qdim, bool cell_data) {
    write_mesh();
    size_type nb_val = 0;
    if (cell_data) {
      switch_to_cell_data();
      nb_val = psl ? psl->linked_mesh().convex_index().card()
                   : pmf->linked_mesh().convex_index().card();
    } else {
      switch_to_point_data();
      nb_val = psl ? psl->nb_points() : pmf_dof_used.card();
    }
    size_type Q = qdim;
    if (Q == 1) Q = gmm::vect_size(U) / nb_val;
    GMM_ASSERT1(gmm::vect_size(U) == nb_val*Q,
                "inconsistency in the size of the dataset: "
                << gmm::vect_size(U) << " != " << nb_val << "*" << Q);
    write_separ();
    if (Q == 1) {
      os << "SCALARS " << remove_spaces(name) << " float 1\n";
      os << "LOOKUP_TABLE default\n";
      for (size_type i=0; i < nb_val; ++i) {
        write_val(float(U[i]));
      }
    } else if (Q <= 3) {
      os << "VECTORS " << remove_spaces(name) << " float\n";
      for (size_type i=0; i < nb_val; ++i) {
        write_vec(U.begin() + i*Q, Q);
      }
    } else if (Q == gmm::sqr(dim_)) {
      /* tensors : coef are supposed to be stored in FORTRAN order
         in the VTK file, they are written with C (row major) order
       */
      os << "TENSORS " << remove_spaces(name) << " float\n";
      for (size_type i=0; i < nb_val; ++i) {
        write_3x3tensor(U.begin() + i*Q);
      }
    } else GMM_ASSERT1(false, "vtk does not accept vectors of dimension > 3");
    write_separ();
  }


  /** @brief A (quite large) class for exportation of data to IBM OpenDX.

                     http://www.opendx.org/

      This class is more capable than the VTK export, as it is
      possible to export many different meshes/slices, with their
      edges, datasets, and create series of dataset for animations
      etc, in a single '.dx' file.

      Moreover, it is able to reopen a '.dx' file and append new data
      into it.  Hence it is possible, if many time-steps are to be
      saved, to view intermediate results in OpenDX during the
      computation.
   */
  class dx_export {
    std::ostream &os;
    char header[256];
    bool ascii;
    const stored_mesh_slice *psl;
    bool psl_use_merged; /* flag enabled if we merge the points of
                            psl before export */
    std::unique_ptr<mesh_fem> pmf;
    dal::bit_vector pmf_dof_used;
    std::vector<unsigned> pmf_cell_type;
    std::fstream real_os;
    dim_type dim_, connections_dim;
    struct dxSeries {
      std::string name;
      std::list<std::string> members;
    };
    struct dxObject {
      std::string name;
      std::string mesh;
    };
    struct dxMesh {
      unsigned flags;
      typedef enum { NONE=0, WITH_EDGES=1, STRUCTURE_WRITTEN=2 } flags_t;
      std::string name;
      dxMesh() : flags(NONE) {}
    };
    std::list<dxObject> objects;
    std::list<dxSeries> series;
    std::list<dxMesh> meshes;
    bool header_written;
  public:
    dx_export(const std::string& fname, bool ascii_ = false,
              bool append_ = false);
    dx_export(std::ostream &os_, bool ascii_ = false);
    ~dx_export(); /* the file is not complete until the destructor
                     has been executed */
    void exporting(const mesh& m, std::string name = std::string());
    void exporting(const mesh_fem& mf, std::string name = std::string());
    void exporting(const stored_mesh_slice& sl, bool merge_points = true,
                   std::string name = std::string());
    /** append edges information (if you want to draw the mesh and are
        using a refined slice. Should be called just after exporting(..)  */
    void exporting_mesh_edges(bool with_slice_edge = true);

    /** the header is the second line of text in the exported file,
       you can put whatever you want -- call this before any write_dataset
       or write_mesh */
    void set_header(const std::string& s);
    void write_mesh();
    /** add an object (typically the name of a data field) to a
       'series', i.e.  an aggregate of consecutive objects. Using
       'series' is useful for animations in opendx

       If 'field_name' corresponds to a data_set whose mesh edges have
       been exported, a second series called serie_name + '_edges'
       will be filled, which will allow you to view the mesh edges.
    */
    void serie_add_object(const std::string& serie_name,
                          const std::string& object_name);
    void serie_add_object(const std::string& serie_name)
    { serie_add_object(serie_name, current_data_name()); }
    /** return the name of current mesh (use exporting(...) to change
        the current mesh) */
    std::string current_mesh_name() { return current_mesh().name; }
    /** return the name of last written data_set */
    std::string current_data_name() { return current_data().name; }
    template<class VECT> void
    write_point_data(const getfem::mesh_fem &mf,
                     const VECT& U0, std::string name = std::string());
    template<class VECT> void
    write_sliced_point_data(const VECT& Uslice,
                            std::string name = std::string());
    /* TOBEDONE !!!!!!!!!!!
       template<class VECT> void
    write_cell_data(const VECT& U, std::string name = std::string());
    void write_mesh_quality(const mesh &m);*/
    void write_normals();
    const stored_mesh_slice& get_exported_slice() const;
    const mesh_fem& get_exported_mesh_fem() const;

  private:
    void init();
    void reread_metadata();
    void update_metadata(std::ios::pos_type);
    void write_series();
    void serie_add_object_(const std::string &serie_name,
                           const std::string &object_name);
    void write_separ();
    std::string default_name(std::string s, int count,
                             const char *default_prefix) {
      if (s.size() == 0) {
        std::stringstream ss; ss << default_prefix << count; return ss.str();
      } else return s;
    }
    template<class T> void write_val(T v) {
      if (ascii) os << " " << v;
      else os.write((char*)&v, sizeof(T));
    }
    static const char* endianness() {
      static int i=0x12345678;
      char *p = (char*)&i;
      if (*p == 0x12) return "msb";
      else if (*p == 0x78) return "lsb";
      else return "this is very strange..";
    }
    bool new_mesh(std::string &name);
    std::list<dxMesh>::iterator get_mesh(const std::string& name,
                                         bool raise_error = true);
    std::list<dxObject>::iterator get_object(const std::string& name,
                                             bool raise_error = true);
    dxMesh &current_mesh() {
      if (meshes.size()) return meshes.back();
      else GMM_ASSERT1(false, "no mesh!");
    }
    dxObject &current_data() {
      if (objects.size()) return objects.back();
      else GMM_ASSERT1(false, "no data!");
    }

    std::string name_of_pts_array(const std::string &meshname)
    { return meshname + std::string("_pts"); }
    std::string name_of_conn_array(const std::string &meshname)
    { return meshname + std::string("_conn"); }
    std::string name_of_edges_array(const std::string &meshname)
    { return meshname + std::string("_edges"); }
    void check_header();
    const char *dxname_of_convex_structure(bgeot::pconvex_structure cvs);
    void write_convex_attributes(bgeot::pconvex_structure cvs);
    void write_mesh_structure_from_slice();
    void write_mesh_structure_from_mesh_fem();
    void write_mesh_edges_from_slice(bool with_slice_edge);
    void write_mesh_edges_from_mesh();
    template <class VECT>
    void smooth_field(const VECT& U, base_vector &sU);
    template<class VECT>
    void write_dataset_(const VECT& U, std::string name, bool cell_data=false);
  };

  template <class VECT>
  void dx_export::smooth_field(const VECT& U, base_vector &sU) {
    size_type Q = gmm::vect_size(U) / psl->nb_points();
    sU.clear(); sU.resize(Q*psl->nb_merged_nodes());
    for (size_type i=0; i < psl->nb_merged_nodes(); ++i) {
      for (size_type j=0; j < psl->merged_point_cnt(i); ++j)
        for (size_type q=0; q < Q; ++q)
          sU[i*Q+q] += U[psl->merged_point_nodes(i)[j].pos*Q+q];
      for (size_type q=0; q < Q; ++q)
        sU[i*Q+q] /= double(psl->merged_point_cnt(i));
    }
  }

  template<class VECT>
  void dx_export::write_point_data(const getfem::mesh_fem &mf, const VECT& U,
                                   std::string name) {
    size_type Q = (gmm::vect_size(U) / mf.nb_dof())*mf.get_qdim();
    if (psl) {
      std::vector<scalar_type> Uslice(Q*psl->nb_points());
      psl->interpolate(mf, U, Uslice);
      write_sliced_point_data(Uslice,name);
    } else {
      std::vector<scalar_type> V(pmf->nb_dof() * Q);
      if (&mf != &(*pmf)) {
        interpolation(mf, *pmf, U, V);
      } else gmm::copy(U,V);
      size_type cnt = 0;
      for (dal::bv_visitor d(pmf_dof_used); !d.finished(); ++d, ++cnt) {
        if (cnt != d)
          for (size_type q=0; q < Q; ++q) {
            V[cnt*Q + q] = V[d*Q + q];
          }
      }
      V.resize(Q*pmf_dof_used.card());
      write_dataset_(V, name);
    }
  }

  template<class VECT> void
  dx_export::write_sliced_point_data(const VECT& Uslice, std::string name) {
    if (!psl_use_merged)
      write_dataset_(Uslice, name, false);
    else {
      base_vector Umerged; smooth_field(Uslice,Umerged);
      write_dataset_(Umerged, name, false);
    }
  }

  template<class VECT> void
  dx_export::write_dataset_(const VECT& U, std::string name, bool cell_data) {
    write_mesh();
    objects.push_back(dxObject());
    name = default_name(name, int(objects.size()), "gf_field");
    objects.back().name = name;
    objects.back().mesh = current_mesh_name();
    size_type nb_val = 0;
    if (cell_data) {
      nb_val = psl ? psl->linked_mesh().convex_index().card()
                   : pmf->linked_mesh().convex_index().card();
    } else {
      nb_val = psl ? (psl_use_merged ? psl->nb_merged_nodes() : psl->nb_points())
                   : pmf_dof_used.card();
    }
    size_type Q = gmm::vect_size(U) / nb_val;
    GMM_ASSERT1(gmm::vect_size(U) == nb_val*Q,
                "inconsistency in the size of the dataset: "
                << gmm::vect_size(U) << " != " << nb_val << "*" << Q);

    os << "\nobject \"" << name << "_data\" class array type float rank ";
    if (Q == 1) { os << "0"; } /* scalar data */
    else if (Q == 4) { os << "2 shape 2 2"; } /* or 2x2 tensor data */
    else if (Q == 9) { os << "2 shape 3 3"; } /* or 2x2 tensor data */
    else { os << "1 shape " << Q; } /* fallback: vector data */
    os << " items " << nb_val;
    if (!ascii) os << " " << endianness() << " binary";
    os << " data follows" << endl;
    for (size_type i=0; i < nb_val*Q; ++i) {
      write_val(float(U[i]));
      if (((i+1) % (Q > 1 ? Q : 10)) == 0) write_separ();
    }
    write_separ();

    if (!cell_data)
      os << "\n  attribute \"dep\" string \"positions\"\n";
    else os << "\n  attribute \"dep\" string \"connections\"\n";
    os << "\n";

    if (current_mesh().flags & dxMesh::WITH_EDGES) {
      os << "\nobject \"" << name << "_edges\" class field\n"
         << "  component \"positions\" value \""
         << name_of_pts_array(current_mesh_name()) << "\"\n"
         << "  component \"connections\" value \""
         << name_of_conn_array(name_of_edges_array(current_mesh_name()))
         << "\"\n"
         << "  component \"data\" value \"" << name << "_data\"\n";
    }

    /* write footer */
    os << "\nobject \"" << name << "\" class field\n"
       << "  component \"positions\" value \""
       << name_of_pts_array(current_mesh_name()) << "\"\n"
       << "  component \"connections\" value \""
       << name_of_conn_array(current_mesh_name()) << "\"\n"
       << "  component \"data\" value \"" << name << "_data\"\n";
  }

  /** @brief POS export.

      export class to Gmsh post-processing file format.

      ( http://geuz.org/gmsh )

      A pos_export can store multiple scalar/vector/tensor fields.
  */

  class pos_export {
  protected:
    std::ostream& os;
    char header[256];

    std::vector<std::vector<float> > pos_pts;
    std::vector<unsigned> pos_cell_type;
    std::vector<std::vector<unsigned> > pos_cell_dof;

    std::unique_ptr<mesh_fem> pmf;
    const stored_mesh_slice *psl;

    size_type view;
    dim_type dim;
    enum { EMPTY, HEADER_WRITTEN, STRUCTURE_WRITTEN, IN_CELL_DATA} state;
    std::ofstream real_os;

  public:
    typedef enum {
                   POS_PT = 0, // point
                   POS_LN = 1, // line
                   POS_TR = 2, // triangles
                   POS_QU = 3, // quadrangles
                   POS_SI = 4, // tetrahedra
                   POS_HE = 5, // hexahedra
                   POS_PR = 6, // prisms
                   POS_PY = 7  // pyramids
    } pos_cell_types;

    pos_export(const std::string& fname);
    pos_export(std::ostream& osname);

    void set_header(const std::string& s);

    void exporting(const mesh& m);
    void exporting(const mesh_fem& mf);
    void exporting(const stored_mesh_slice& sl);

    void write(const mesh& m, const std::string& name="");
    void write(const mesh_fem& mf, const std::string& name="");
    void write(const stored_mesh_slice& sl, const std::string& name="");

    template <class VECT>
    void write(const mesh_fem& mf,const VECT& U, const std::string& name);
    template <class VECT>
    void write(const stored_mesh_slice& sl,const VECT& U, const std::string& name);

  private:
    void init();
    void check_header();

    template <class VECT>
    void write(const VECT& V, const size_type qdim_v);

    template <class VECT>
    void write_cell(const int& t, const std::vector<unsigned>& dof,
                                  const VECT& val);
  };

  template <class VECT>
  void pos_export::write(const mesh_fem& mf,const VECT& U,
                         const std::string& name){
    check_header();
    exporting(mf);

    os << "View \"" << name.c_str() <<"\" {\n";

    size_type nb_points = mf.nb_dof()/mf.get_qdim();
    size_type qdim_u = gmm::vect_size(U)/nb_points;
    if (psl){
      std::vector<scalar_type> Uslice(psl->nb_points()*qdim_u);
      psl->interpolate(mf, U, Uslice);
      qdim_u = gmm::vect_size(Uslice)/psl->nb_points();
      write(Uslice, qdim_u);
    }else {
      std::vector<scalar_type> V(pmf->nb_dof()*qdim_u);
      if (&mf != &(*pmf)) {
        interpolation(mf, *pmf, U, V);
      } else gmm::copy(U,V);
      /*for (dal::bv_visitor d(pmf_dof_used); !d.finished(); ++d, ++cnt) {
        if (cnt != d)
          for (size_type q=0; q < Q; ++q) {
            V[cnt*Q + q] = V[d*Q + q];
          }
      }
      V.resize(Q*pmf_dof_used.card());*/
      nb_points = pmf->nb_dof()/pmf->get_qdim();
      qdim_u = gmm::vect_size(V)/nb_points;
      write(V, qdim_u);
    }

    os << "};\n";
    os << "View[" << view << "].ShowScale = 1;\n";
    os << "View[" << view << "].ShowElement = 0;\n";
    os << "View[" << view << "].DrawScalars = 1;\n";
    os << "View[" << view << "].DrawVectors = 1;\n";
    os << "View[" << view++ << "].DrawTensors = 1;\n";
  }

  template <class VECT>
  void pos_export::write(const stored_mesh_slice& sl,const VECT& V,
                         const std::string& name){
    check_header();
    exporting(sl);

    os << "View \"" << name.c_str() <<"\" {\n";

    size_type qdim_v = gmm::vect_size(V)/psl->nb_points();
    write(V, qdim_v);

    os << "};\n";
    os << "View[" << view << "].ShowScale = 1;\n";
    os << "View[" << view << "].ShowElement = 0;\n";
    os << "View[" << view << "].DrawScalars = 1;\n";
    os << "View[" << view << "].DrawVectors = 1;\n";
    os << "View[" << view++ << "].DrawTensors = 1;\n";
  }

  template <class VECT>
  void pos_export::write(const VECT& V, const size_type qdim_v) {
    int t;
    std::vector<unsigned> cell_dof;
    std::vector<scalar_type> cell_dof_val;
    for (size_type cell = 0; cell < pos_cell_type.size(); ++cell) {
      t = pos_cell_type[cell];
      cell_dof = pos_cell_dof[cell];
      cell_dof_val.resize(cell_dof.size()*qdim_v, scalar_type(0));
      for (size_type i=0; i< cell_dof.size(); ++i)
        for (size_type j=0; j< qdim_v; ++j)
          cell_dof_val[i*qdim_v+j] = scalar_type(V[cell_dof[i]*qdim_v+j]);
      write_cell(t,cell_dof,cell_dof_val);
    }
  }

  template <class VECT>
  void pos_export::write_cell(const int& t, const std::vector<unsigned>& dof,
                                            const VECT& val) {
    size_type qdim_cell = val.size()/dof.size();
    size_type dim3D = size_type(-1);
    if (1==qdim_cell){
      dim3D = size_type(1);
      os << "S";
    } else if (2==qdim_cell || 3==qdim_cell){
      dim3D = size_type(3);
      os << "V";
    } else if (4<=qdim_cell && qdim_cell<=9){
      dim3D = size_type(9);
      os << "T";
    }
    switch (t){
      case POS_PT: os << "P("; break; // point
      case POS_LN: os << "L("; break; // line
      case POS_TR: os << "T("; break; // triangle
      case POS_QU: os << "Q("; break; // quadrangle
      case POS_SI: os << "S("; break; // tetrahedra (simplex)
      case POS_HE: os << "H("; break; // hexahedra
      case POS_PR: os << "I("; break; // prism
      case POS_PY: os << "Y("; break; // pyramid
    }
    for (size_type i=0; i<dof.size(); ++i){
      for(size_type j=0; j<dim; ++j){
        if(0!=i || 0!=j) os << ",";
        os << pos_pts[dof[i]][j];
      }
      for (size_type j=dim; j<3; ++j){
        os << ",0.00";
      }
    }

    os << "){";
    for (size_type i=0; i<dof.size(); ++i){
      for(size_type j=0; j<qdim_cell; ++j){
        if(0!=i || 0!=j) os << ",";
        os << val[i*qdim_cell+j];
      }
      for (size_type j=qdim_cell; j< dim3D; ++j){
        os << ",0.00";
      }
    }
    os << "};\n";
  }
}  /* end of namespace getfem. */

#endif /* GETFEM_EXPORT_H__  */